Askiitians Tutor Team
Last Activity: 5 Months ago
Let's break down the problem of the parallel plate capacitor with multiple plates and see how we can find the total capacitance of the arrangement. This is a fascinating topic in electrostatics, and understanding it will give you a solid grasp of capacitors in general.
Understanding the Configuration
In this scenario, we have 10 metallic plates stacked together, with a dielectric material between them. The key detail is that alternate plates are connected, which means we can think of the arrangement as a series of capacitors formed between neighboring plates.
Capacitance Between Two Plates
The capacitance \( C \) between two neighboring plates can be expressed using the formula:
C = \frac{\varepsilon A}{d}
where:
- \(\varepsilon\) is the permittivity of the dielectric material between the plates,
- A is the area of the plates, and
- d is the distance between the plates.
Analyzing the Connections
Since alternate plates are connected, we can visualize the arrangement as a series of capacitors. For 10 plates, there are 9 pairs of neighboring plates, each forming a capacitor with capacitance \( C \). The pairs are as follows:
- Plate 1 and Plate 2
- Plate 3 and Plate 4
- Plate 5 and Plate 6
- Plate 7 and Plate 8
- Plate 9 and Plate 10
Calculating Total Capacitance
When capacitors are connected in series, the total capacitance \( C_{total} \) can be calculated using the formula:
\(\frac{1}{C_{total}} = \frac{1}{C_1} + \frac{1}{C_2} + \ldots + \frac{1}{C_n}\)
In our case, since each capacitor has the same capacitance \( C \), this simplifies to:
\(\frac{1}{C_{total}} = \frac{9}{C}\)
Thus, we can rearrange this to find \( C_{total} \):
C_{total} = \frac{C}{9}
Final Answer
Therefore, the total capacitance of the combination of the plates is \( \frac{C}{9} \). So, the correct option is b) C/9.
This example illustrates how understanding the configuration and connections of capacitors can help in calculating total capacitance. If you have any further questions or need clarification on any part of this, feel free to ask!
